Algebra 1: Factoring Practice Flashcards
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Questions and Answers

What is the factorization of $72x^7y^2 - 16x^2y^3$?

  • 8y²(9x^7 - 2x²)
  • 2x^2(36x^5y - 8y²)
  • 8x²y²(9x⁵ - 2y) (correct)
  • 4x³y(18x^4 - 4y²)

    • What is the factorization of $-9y^9 - 18y^9x^2$?

  • -9y⁹(1 + 2x²) (correct)
  • -9y²(1 + 2yx²)
  • -18y^9(x + 1)
  • -9y^8(1 + 2xy)

    • What is the factorization of $20a^4b^5 + 8a^5b - 4a^3b$?

  • 2a²b(10a^2b^4 + 4a - 2)
  • 4a³b(5ab⁴ + 2a - 1)
  • 8a²b²(2.5ab³ + a - 0.5)
  • 4a³b(5ab⁴ + 2a² - 1) (correct)

    • What is the factorization of $x^4 + 3x^2 - 7x$?

    <p>x(x³ + 3x - 7)</p> Signup and view all the answers

    What is the factorization of $x^3 + 3x^2 + 4x + 12$?

    <p>(x² + 4)(x + 3)</p> Signup and view all the answers

    What is the factorization of $25xy + 30x - 30y - 36$?

    <p>(5x - 6)(5y + 6)</p> Signup and view all the answers

    What does Prime mean in factoring context?

    <p>When you try grouping, the two sets of parentheses do not match.</p> Signup and view all the answers

    What is the factorization of $16x^3 + 8x^2 + 8x + 4$?

    <p>4(2x² + 1)(2x + 1)</p> Signup and view all the answers

    What is the factorization of $n^2 - 8n + 7$?

    <p>(n - 7)(n - 1)</p> Signup and view all the answers

    What is the factorization of $x^2 - 6x + 4$?

    <p>Prime</p> Signup and view all the answers

    What is the factorization of $n^2 - 2n - 35$?

    <p>(n + 5)(n - 7)</p> Signup and view all the answers

    What is the factorization of $3x^2 - 15x + 12$?

    <p>3(x - 1)(x - 4)</p> Signup and view all the answers

    What is the factorization of $6x^2 - 42x - 108$?

    <p>6(x - 9)(x + 2)</p> Signup and view all the answers

    What is the factorization of $5x^2 + 27x + 10$?

    <p>(5x + 2)(x + 5)</p> Signup and view all the answers

    What is the factorization of $5v^2 - 23v + 12$?

    <p>(5v - 3)(v - 4)</p> Signup and view all the answers

    What is the factorization of $6k^2 - 3k - 9$?

    <p>3(2k - 3)(k + 1)</p> Signup and view all the answers

    What is the factorization of $10n^2 - 26n + 12$?

    <p>2(5n - 3)(n - 2)</p> Signup and view all the answers

    What is the factorization of $25m^2 - 1$?

    <p>(5m + 1)(5m - 1)</p> Signup and view all the answers

    What is the factorization of $16r^2 + 8r + 1$?

    <p>(4r + 1)²</p> Signup and view all the answers

    What is the factorization of $9k^2 - 12k + 4$?

    <p>(3k - 2)²</p> Signup and view all the answers

    What does Prime mean in the context of polynomials?

    <p>All of the above</p> Signup and view all the answers

    What is the factorization of $4x² + 13x + 9$?

    <p>(x + 1)(4x + 9)</p> Signup and view all the answers

    What is the factorization of $3n^2 - 75$?

    <p>3(n + 5)(n - 5)</p> Signup and view all the answers

    What is the factorization of $100b^2 + 120b + 36$?

    <p>4(5b + 3)²</p> Signup and view all the answers

    What is the factorization of $18a² - 24a + 8$?

    <p>2(3a - 2)²</p> Signup and view all the answers

    What is the factorization of $2x³ + 7x² - 2x - 7$?

    <p>(x-1)(x+1)(2x+7)</p> Signup and view all the answers

    What is the factorization of $12x³ - 20x² - 3x + 5$?

    <p>(2x-1)(2x+1)(3x-5)</p> Signup and view all the answers

    Study Notes

    Factoring Basics

    • Factoring involves rewriting expressions as the product of their factors.
    • The greatest common factor (GCF) is the highest factor shared among terms.

    Types of Factorization

    • GCF Only: Some expressions can be factored by identifying a common factor among all terms.
    • Factor by Grouping: Typically used for polynomials that can be grouped into pairs with common factors.
    • Trinomials: Quadratic expressions can often be factored into two binomials, especially when the leading coefficient (LC) is 1.
    • Special Cases: Certain forms, such as perfect square trinomials and differences of squares, follow specific factoring patterns.

    Examples of Factoring

    • GCF Examples:

      • ( 8x²y²(9x⁵ - 2y) ) becomes ( 72x⁷y² - 16x²y³ ).
      • ( -9y⁹(1 + 2x²) ) leads to ( -9y⁹ - 18y⁹x² ).

    • Trinomial Factoring:

      • ( n² - 8n + 7 ) is factored using ( (n - 7)(n - 1) ).
      • ( n² - 2n - 35 ) factors to ( (n + 5)(n - 7) ).

    • Special Cases:

      • The expression ( (5m + 1)(5m - 1) ) applies the difference of squares to yield ( 25m² - 1 ).
      • ( (4r + 1)² ) expands to ( 16r² + 8r + 1 ) (perfect square trinomial).

    Identifying Prime Expressions

    • Certain expressions cannot be factored further, labeled as "Prime," like ( x² - 6x + 4 ) where no pairs of numbers multiply to 4 and add to -6.

    Application of GCF and Special Cases

    • Problems often combine GCF with special cases: ( 3(n + 5)(n - 5) ) simplifies to ( 3n² - 75 ) combining the difference of squares with GCF.

    Summary of Key Techniques

    • Recognize the structure of the polynomial to determine the best factoring method.
    • Different methods may apply to the same polynomial depending on its form, such as grouping, recognizing trinomials, or applying GCF first.
    • Practicing various factoring methods helps in identifying the quickest path to the solution for polynomials.

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    Test your skills in factoring expressions with these flashcards designed for Algebra 1. Each card presents a problem to factor completely, focusing on the Greatest Common Factor (GCF). Use these cards to solidify your understanding and improve your algebra skills.

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